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Techniques and Tools for the Analysis ofTimed Workflows
Jiri Srba
Department of Computer Science, Aalborg University,Selma Lagerlofs Vej 300, 9220 Aalborg East, Denmark
NWPT’15, Iceland, October 22nd, 2015
Joint work with Peter G. Jensen, Jose A. Mateo and Mathias G. Sørensen.
Workflow Definition
Workflows [Wikipedia]
A workflow consists of
an orchestrated and repeatable pattern of business activity
enabled by the systematic organization of resources intoprocesses that transform materials, provide services, or processinformation.
Examples:
Car assembly line.
Insurance claim.
Blood transfusion.
All these are examples of time-critical workflows.
There is a need for methods and tools for timed workflow analysis.
2 / 26
Workflow Definition
Workflows [Wikipedia]
A workflow consists of
an orchestrated and repeatable pattern of business activity
enabled by the systematic organization of resources intoprocesses that transform materials, provide services, or processinformation.
Examples:
Car assembly line.
Insurance claim.
Blood transfusion.
All these are examples of time-critical workflows.
There is a need for methods and tools for timed workflow analysis.
2 / 26
Introduction — Workflow Nets
Workflow nets by Wil van der Aalst [ICATPN’97] are widelyused for workflow modelling.
Based on Petri nets.
Abstraction from data, focus on execution flow.
Early detection of design errors like deadlocks, livelocks andother abnormal behaviour.
Classical soundness for workflow nets:
option to complete,proper termination, andabsence of redundant tasks.
3 / 26
Focus of the Talk
Theory of workflow nets based on timed-arc Petri nets.
Definition of soundness and strong soundness.
Results about decidability/undecidability of soundness.
Minimum and maximum execution time of workflow nets.
Integration within the tool TAPAAL and case studies.
Discrete vs. continuous time.
4 / 26
Timed-Arc Petri Net: Booking/Payment Example
0
in
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
0
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
1
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
2
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
5
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
5
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
8
inv: ≤ 10
payment
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
0
successful
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
0
out
start
book pay
success
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
start
book pay
restart restart success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
0
in
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
0
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
0 0 0attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
2
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
2 2 2attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
0
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
2 2attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
3
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
out
5 5attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
3
inv: ≤ 10
payment
successful
out
7 7attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
5
inv: ≤ 10
payment
successful
out
9 9attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
0
successful
out
9 9attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
0
successful
out
9attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
0
successful
out
attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Timed-Arc Petri Net: Booking/Payment Example
in
inv: ≤ 5
booking
inv: ≤ 10
payment
successful
0
out
attempts
start 3×
book pay
restart restart empty success
fail
[5,5]
fail
[10,10]
[2, 5]
5 / 26
Monotonic Timed-Arc Petri Nets
Timed-Arc Petri Nets (TAPN) Modelling Features:
Timed tokens, intervals (guards) on arcs.
Weighted arcs.
Transport arcs.
Inhibitor arcs.
Age invariants.
Urgent transitions.
Monotonic Timed-Arc Petri Nets (MTAPN)
No inhibitor arcs, no age invariants, no urgent transitions.
We consider the integer-delay (discrete-time) semantics (for now).
6 / 26
Monotonic Timed-Arc Petri Nets
Timed-Arc Petri Nets (TAPN) Modelling Features:
Timed tokens, intervals (guards) on arcs.
Weighted arcs.
Transport arcs.
Inhibitor arcs.
Age invariants.
Urgent transitions.
Monotonic Timed-Arc Petri Nets (MTAPN)
No inhibitor arcs, no age invariants, no urgent transitions.
We consider the integer-delay (discrete-time) semantics (for now).
6 / 26
Marking Extrapolation
Marking in TAPN
M : P → B(N0)
Problem
Infinitely many markings even for bounded nets.
We define cut(M) extrapolation for a marking M:
compute for each place maximum relevant token ages
Cmax : P → (N0 ∪ {−1})
change the age of each token in place p exceeding the boundCmax(p) into Cmax(p) + 1.
7 / 26
Monotonicity Lemma for MTAPN
Monotonicity Lemma (t is transition, d is delay)
Let M and M ′ be markings in an MTAPN s.t. cut(M) v cut(M ′).
If Mt−→ M1 then M ′
t−→ M ′1 and cut(M1) v cut(M ′1).
If Md−→ M1 then M ′
d−→ M ′1 and cut(M1) v cut(M ′1).
Fact: inhibitor arcs, age invariants and urgency break monotonicity.
8 / 26
Timed-Arc Workflow Net
Definition
A TAPN is called a timed-arc workflow net if
it has a unique place in ∈ P s.t. •in = ∅ and in• 6= ∅,it has a unique place out ∈ P s.t. out• = ∅ and •out 6= ∅,•p 6= ∅ and p• 6= ∅ for all p ∈ P \ {in, out}, and•t 6= ∅ for all t ∈ T .
in outstart working
inv: ≤ 10
finish[5, 10]
An initial marking has just one token of age 0 in the place in.
A final marking has exactly one token in place out and allother places are empty.
9 / 26
Timed-Arc Workflow Net
Definition
A TAPN is called a timed-arc workflow net if
it has a unique place in ∈ P s.t. •in = ∅ and in• 6= ∅,it has a unique place out ∈ P s.t. out• = ∅ and •out 6= ∅,•p 6= ∅ and p• 6= ∅ for all p ∈ P \ {in, out}, and•t 6= ∅ for all t ∈ T .
in outstart working
inv: ≤ 10
finish[5, 10]
An initial marking has just one token of age 0 in the place in.
A final marking has exactly one token in place out and allother places are empty.
9 / 26
Timed-Arc Workflow Net
Definition
A TAPN is called a timed-arc workflow net if
it has a unique place in ∈ P s.t. •in = ∅ and in• 6= ∅,it has a unique place out ∈ P s.t. out• = ∅ and •out 6= ∅,•p 6= ∅ and p• 6= ∅ for all p ∈ P \ {in, out}, and•t 6= ∅ for all t ∈ T .
0
in outstart working
inv: ≤ 10
finish[5, 10]
An initial marking has just one token of age 0 in the place in.
A final marking has exactly one token in place out and allother places are empty.
9 / 26
Timed-Arc Workflow Net
Definition
A TAPN is called a timed-arc workflow net if
it has a unique place in ∈ P s.t. •in = ∅ and in• 6= ∅,it has a unique place out ∈ P s.t. out• = ∅ and •out 6= ∅,•p 6= ∅ and p• 6= ∅ for all p ∈ P \ {in, out}, and•t 6= ∅ for all t ∈ T .
in outstart
0
working
inv: ≤ 10
finish[5, 10]
An initial marking has just one token of age 0 in the place in.
A final marking has exactly one token in place out and allother places are empty.
9 / 26
Timed-Arc Workflow Net
Definition
A TAPN is called a timed-arc workflow net if
it has a unique place in ∈ P s.t. •in = ∅ and in• 6= ∅,it has a unique place out ∈ P s.t. out• = ∅ and •out 6= ∅,•p 6= ∅ and p• 6= ∅ for all p ∈ P \ {in, out}, and•t 6= ∅ for all t ∈ T .
in outstart
7
working
inv: ≤ 10
finish[5, 10]
An initial marking has just one token of age 0 in the place in.
A final marking has exactly one token in place out and allother places are empty.
9 / 26
Timed-Arc Workflow Net
Definition
A TAPN is called a timed-arc workflow net if
it has a unique place in ∈ P s.t. •in = ∅ and in• 6= ∅,it has a unique place out ∈ P s.t. out• = ∅ and •out 6= ∅,•p 6= ∅ and p• 6= ∅ for all p ∈ P \ {in, out}, and•t 6= ∅ for all t ∈ T .
in
0
outstart working
inv: ≤ 10
finish[5, 10]
An initial marking has just one token of age 0 in the place in.
A final marking has exactly one token in place out and allother places are empty.
9 / 26
Soundness of Timed-Arc Workflow Nets
Definition
A timed-arc workflow net is sound if for any marking M reachablefrom the initial marking holds:
1 from M it is possible to reach some final marking, and
2 if M(out) contains a token then M is a final marking.
Soundness Implies Boundedness
If N is a sound and monotonic timed-arc workflow net then N isbounded.
10 / 26
Soundness of Timed-Arc Workflow Nets
Definition
A timed-arc workflow net is sound if for any marking M reachablefrom the initial marking holds:
1 from M it is possible to reach some final marking, and
2 if M(out) contains a token then M is a final marking.
Soundness Implies Boundedness
If N is a sound and monotonic timed-arc workflow net then N isbounded.
10 / 26
Sound and Unbounded Net with Age Invariants
in
p1
inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
0
in
p1
inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
0
p1
inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
0
p1
0 inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
0
p1
0 0 inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
0
p1
0 inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
0
p1
inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
1
p1
inv: ≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
p1
inv: ≤ 0
p2
0
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Sound and Unbounded Net with Age Invariants
in
p1
////inv://////≤ 0
p2
out
t1
[0, 0]
[1,∞]
t2
Sound and Unbounded Net with Urgent Transitions
Remove age invariant ≤ 0 at place p2 and make t2 urgent.
11 / 26
Decidability of Soundness
Theorem
Soundness is undecidable for timed-arc workflow nets.
Undecidable even for monotonic nets with only inhibitor arcs, oronly age invariants, or only urgent transitions.
Theorem
Soundness is decidable for
bounded timed-arc workflow nets, and for
monotonic timed-arc workflow nets.
Proof: Forward and backward search through the extrapolatedstate-space (using the function cut). Termination for MTAPN dueto the monotonicity lemma.
12 / 26
Decidability of Soundness
Theorem
Soundness is undecidable for timed-arc workflow nets.
Undecidable even for monotonic nets with only inhibitor arcs, oronly age invariants, or only urgent transitions.
Theorem
Soundness is decidable for
bounded timed-arc workflow nets, and for
monotonic timed-arc workflow nets.
Proof: Forward and backward search through the extrapolatedstate-space (using the function cut). Termination for MTAPN dueto the monotonicity lemma.
12 / 26
Compare Decidability of Soundness with Reachability
Notice that for the subclass of monotonic timed-arc Petri nets
reachability is undecidable [Ruiz, Gomez, Escrig’99], but
soundness is decidable.
Question
Is soundness always sufficient for timed workflows?
13 / 26
Compare Decidability of Soundness with Reachability
Notice that for the subclass of monotonic timed-arc Petri nets
reachability is undecidable [Ruiz, Gomez, Escrig’99], but
soundness is decidable.
Question
Is soundness always sufficient for timed workflows?
13 / 26
Customer Complaint Workflow
in out
start
req info provide info
decision
Sound workflow, no timing information, no progress.
14 / 26
Customer Complaint Workflow
in
inv ≤ 14
out
inv ≤ 14
start
req info provide info
decision
Progress is ensured, infinite time-divergent behaviour.
14 / 26
Customer Complaint Workflow
in
inv ≤ 14
out
inv ≤ 14
start
req info provide info
decision
Strongly sound workflow with time-bounded execution.
14 / 26
Strong Soundness
Definition
A timed-arc workflow net is strongly sound if
it is sound,
has no time-divergent markings (except for the final ones), and
every infinite computation is time-bounded.
We can define maximum execution time for strongly sound nets.
Theorem
Strong soundness of timed-arc workflow nets is undecidable.
Theorem
Strong soundness of bounded timed-arc workflow nets is decidable.
Proof: By reduction to reachability on timed-arc Petri nets.
15 / 26
Strong Soundness
Definition
A timed-arc workflow net is strongly sound if
it is sound,
has no time-divergent markings (except for the final ones), and
every infinite computation is time-bounded.
We can define maximum execution time for strongly sound nets.
Theorem
Strong soundness of timed-arc workflow nets is undecidable.
Theorem
Strong soundness of bounded timed-arc workflow nets is decidable.
Proof: By reduction to reachability on timed-arc Petri nets.
15 / 26
Decidability of Strong Soundness (Proof Sketch)
Perform normal soundness check and remember the size S ofits state-space (in the extrapolated semantics).
Let B be the maximum possible delay in any marking.
Check if the given workflow net can delay more thanU = S · B + 1 time units before reaching a final marking.
If yes, it is not strongly sound.If no, it is strongly sound.
0
in out
0
timer
inv: ≤ U
late nok
workflow net N
tick
[U,U]
ok
ups
16 / 26
Implementation and Experiments
All algorithms implemented within TAPAAL (www.tapaal.net).
Publicly available and open-source.
Graphical editor with components, visual simulator.
Efficient engine implementation (including furtheroptimizations).
Case studies:
Break System Control Unit, a part of the SAE standardARP4761 (certification of civil aircrafts).
MPEG-2 encoding algorithm on multi-core processors.
Blood transfusion workflow, a larger benchmarking case-studydescribed in little-JIL workflow language.
Home automation system for light control in a family housewith 16 lights/25 buttons, motion sensors and alarm.
17 / 26
TAPAAL Verification of Break System Control Unit
18 / 26
TAPAAL Verification of Break System Control Unit
18 / 26
Recent TAPAAL Development
TAPAAL is being continuously improved and extended(MPEG-2 workflow analysis with two B-frames took 10s lastyear, now it takes only 1.4s).
Memory preserving data structure PTrie.
MPEG-2 with three B-frames
soundness strong soundness
no PTrie 33s / 1071MB 30s / 970MB
PTrie 42s / 276MB 45s / 191MB
Approximate analysis (smaller constants, less precision).
Compositional, resource-aware analysis.
19 / 26
Future TAPAAL Development
Resources with quantitative aspects (cost, energy).
Two player timed workflow games (also with stochasticopponent).
Integration with UPPAAL Stratego.
Workflow analysis in the continuous time semantics.
20 / 26
Continuous Semantics vs. Discrete Semantics
Theorem (For Closed TAPNs)
Let M0 be a marking with integer ages only. If
M0d0,t0−→ M1
d1,t1−→ M2d2,t2−→ . . .
dn−1,tn−1−→ Mn
where di ∈ R≥0 then also
M0d ′0,t0−→ M ′1
d ′1,t1−→ M ′2d ′2,t2−→ . . .
d ′n−1,tn−1−→ M ′n
where d ′i ∈ N0.
We construct a set of linear inequalities that describe allpossible delays allowed in the real-time execution.We only need difference constraints, hence the correspondingmatrix in LP is totally unimodular.As the instance of LP has a real solution, it has also anoptimal integral solution.
21 / 26
Continuous Semantics Implies Discrete Semantics
Theorem
If a timed-arc workflow net is sound in the continuous semanticsthen it is also sound in the discrete semantics.
Proof:
Let N be sound in the continuous semantics.
Let M be a marking reachable from the initial marking Min inthe discrete semantics.
Hence some final marking Mout is reachable from M in thecontinuous semantics.
We can conclude using the theorem that a marking M ′out withthe same distribution of tokens as Mout is reachable from Malso in the discrete semantics.
22 / 26
Discrete Semantics Implies Continuous Semantics
Theorem
If a timed-arc workflow net with no age invariants and no urgenttransitions is sound in the discrete semantics then it is sound alsoin the continuous semantics.
Proof:
We can arbitrarily delay in any marking.
Hence the token ages exceed the maximum constants.
Now there is no difference between discrete and continuoussemantics.
The theorem does not hold for general timed-arc workflow nets.
23 / 26
Discrete Semantics Implies Continuous Semantics
Theorem
If a timed-arc workflow net with no age invariants and no urgenttransitions is sound in the discrete semantics then it is sound alsoin the continuous semantics.
Proof:
We can arbitrarily delay in any marking.
Hence the token ages exceed the maximum constants.
Now there is no difference between discrete and continuoussemantics.
The theorem does not hold for general timed-arc workflow nets.
23 / 26
Continuous Semantics Challenge
0
in out
waiting
deadline
inv: ≤ 1
finished
init
service
late
early
[0, 0]
[1, 1]
Sound in discrete semantics but unsound in continuous semantics.
24 / 26
Continuous Semantics Challenge
in out
0
waiting
0deadline
inv: ≤ 1
finished
init
service
late
early
[0, 0]
[1, 1]
Sound in discrete semantics but unsound in continuous semantics.
24 / 26
Continuous Semantics Challenge
in out
0.5
waiting
0.5deadline
inv: ≤ 1
finished
init
service
late
early
[0, 0]
[1, 1]
Sound in discrete semantics but unsound in continuous semantics.
24 / 26
Continuous Semantics Challenge
in out
waiting
0.5deadline
inv: ≤ 1
0
finished
init
service
late
early
[0, 0]
[1, 1]
Sound in discrete semantics but unsound in continuous semantics.
24 / 26
Continuous Semantics Challenge
in out
waiting
1deadline
inv: ≤ 1
0.5
finished
init
service
late
early
[0, 0]
[1, 1]
Sound in discrete semantics but unsound in continuous semantics.
24 / 26
Continuous Semantics Summary
Continuous soundness implies discrete soundness.
Opposite implication holds only for nets without urgency.
Strong soundness is not an issue.
Theorem
Let N be a workflow net is sound in the continuous-time semantics.
The net N is strongly sound in the discrete-time semantics iff it isstrongly sound in the continuous-time semantics.
25 / 26
Continuous Semantics Summary
Continuous soundness implies discrete soundness.
Opposite implication holds only for nets without urgency.
Strong soundness is not an issue.
Theorem
Let N be a workflow net is sound in the continuous-time semantics.
The net N is strongly sound in the discrete-time semantics iff it isstrongly sound in the continuous-time semantics.
25 / 26
Conclusion
Framework for the study of timed-arc workflow nets.
Undecidability of soundness and strong soundness.
Efficient algorithms for the decidable subclasses.
Relationship to continuous soundness.
Integration into the tool TAPAAL.
www.tapaal.net
Reachability Formulas:ReachabilityCardinalityComparison
Trophies for the “Known” Models Trophies for the “Surprise” Models
LoLA174 (points)
LoLA optimistic174 (points)
LoLA optimisticincomplete148 (points)
marcie24 (points)
LoLA12 (points)
LoLA optimistic12 (points)
LoLA optimisticincomplete12 (points)
Trophies for All Models
LoLA198 (points)
LoLA optimistic198 (points)
LoLA optimisticincomplete172 (points)
Silver medal at Model Checking Contest 2014 and 2015.(reachability category)
26 / 26
Conclusion
Framework for the study of timed-arc workflow nets.
Undecidability of soundness and strong soundness.
Efficient algorithms for the decidable subclasses.
Relationship to continuous soundness.
Integration into the tool TAPAAL.
www.tapaal.net
Reachability Formulas:ReachabilityCardinalityComparison
Trophies for the “Known” Models Trophies for the “Surprise” Models
LoLA174 (points)
LoLA optimistic174 (points)
LoLA optimisticincomplete148 (points)
marcie24 (points)
LoLA12 (points)
LoLA optimistic12 (points)
LoLA optimisticincomplete12 (points)
Trophies for All Models
LoLA198 (points)
LoLA optimistic198 (points)
LoLA optimisticincomplete172 (points)
Silver medal at Model Checking Contest 2014 and 2015.(reachability category)
26 / 26